If \(u(x)\)  is a convex function, then so is its perspective function \(v(x,y)\)  [1]}.
As a result,
\(t_if_i\!\left(\!\frac{d_{i1}}{t_i}, \frac{d_{i2}}{t_i}\!\right)\!=\!B t_i\!\left(\!a_{i1} 2^{\frac{d_{i1}+d_{i2}}{Bt_i}}+(a_{i2}-a_{i1}) 2^{\frac{d_{i2}}{Bt_i}}-a_{i2}\!\right)\) 
